SAT Math Level 2 - ALGEBRA

Question 1

Difference of Two Squares: X^2 - Y^2 =

Answer 1

( x + y )( x - y )

Question 2

Graph of Quadratic Function: f(x) =

Answer 2

ax^2 + bx + c

Question 3

For the graph of quadratic function, the x-value of the vertex is

Answer 3

x value = -b/2a

Question 4

If y = a(x-h)^2 + k, then the vertex of the parabola is

Answer 4

(h,k)

Question 5

If y = ax^2 + bx + c, the sum of the two roots are

Answer 5

-b/a

Question 6

If y = ax^2 + bx + c, the product of the two roots are

Answer 6

c/a

Question 7

Is 1 a prime number?

Answer 7

NO!

Question 8

1 foot is equal to _____ inches?

Answer 8

12 inches

Question 9

Polynomial

Answer 9

A finite sum of positive integer powers of a variable, often x

Question 10

Degrees in a polynomial

Answer 10

The degree is the highest power of x in the polynomial. etc. 5x^6 + 3x^3 - 5x –> the degree is 6

Question 11

Leading coefficient

Answer 11

The coefficient of the highest power of x

etc. 21x^4 + 10x^6 - 3 –> the leading coefficient is 10

Question 12

Properties of polynomials

Answer 12

• every polynomial is continuous: they have no gaps or holes
• they are smooth everywhere: polynomial graphs don’t have sharp points or cusps
• a degree n polynomial has at most n real roots: it can cross the x-axis in at most n different places
• A degree n polynomial graph has at most (n-1) “bumps” on it (max min point)

Question 13

Not polynomials

Answer 13

1/x, x^2 + square root x and sinx

Question 14

Four quadrants in a plane

Answer 14

• 1st quadrant - x and y positive (upper right)
• 2nd quadrant - x negative and y positive (upper left)
• 3rd quadrant - x and y negative (lower left)
• 4th quadrant - x positive and y negative (lower right)

Question 15

Even degree polynomials

Answer 15

Positive leading coefficient
- graph moves from quadrant 2 to quadrant 1

Negative leading coefficient
- graph moves from quadrant 3 to quadrant 4

Question 16

Odd degree polynomials

Answer 16

Positive leading coefficient
- graph moves from quadrant 3 to quadrant 1

Negative leading coefficient
- graph moves from quadrant 2 to quadrant 4

Question 17

loga(a) =

Answer 17

1

Question 18

loga(1) =

Answer 18

0

Question 19

Change of base formula (Logs)

Answer 19

loga(X) = logb(X) / logb(A)

Question 20

Absolute value

Answer 20

The number “made positive”
etc. | 6 | = 6 , | -7 | = 7
| x | ^2 = | x^2 | = x^2
| x | = | -x |

Question 21

If y varies directly to x then

Answer 21

y = kx
k = constant of proportionality

Question 22

If y varies indirectly to x then

Answer 22

y = k/x
k = constant of proportionality

Question 23

n! =

Answer 23

n x (n - 1) x (n - 2) x ... x 3 x 2 x 1
etc. 6! = 6 x 5 x 4 x 3 x 2 x 1

Question 24

1! =

Answer 24

1

Question 25

0! =

Answer 25

1

Question 26

Vertex

Answer 26

Lowest or Highest point on a parabola